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NEW EXPLANATION 



EBBING AMB FLOWING 



THE SEA, 



^7 PON THE 



PRINCIPLES OF GRAVITATION. 



"0 



Bt g. BENNETT. 



Humanumesterrare Suum cuique tribuito. 



NEW-YORK: 

PUBLISHED FOR THE AUTHOR, 

A5D SOLD BY ALL THE E00KSELLEB8 IS" THE UNITED STATES, 
GOULD AND VAN PELT, PRINTERS, NO, 9 WALL-IIRBET, 

1916. 



^ *? 



t> 



*l 



Southern District of J\*e~A-York, $s. 

Be it bemembeiied, That on the sixteenth day of March, im 
the fortieth year of the Independence of the United States of Ame- 
rica, Samuel Bennett, of the said District, hath deposited in this 
office the title of a Book, the right whereof he claims as Author 
and Proprietor, in the words following, to wit : 

u A New Explanation of the Ebbing and Flowing of the Sea, 
upon the Principles of Gravitation." By S. Bennett. 

n Humanum est errare." 



" Suum cuique tribuito." 

In conformity to the Act of the Congress of the United States, 
entitled " An Act for the encouragement of Learning, by securing 
the copies of Maps, Charts and Books, to the authors and proprie- 
tors of such copies, during' the time therein mentioned." And 
also an Act, entitled " an Act, supplementary to an Act, entitled 
an Act for the encouragement of Learning, by securing the copies 
of Maps, Charts and Books, to the authors and proprietors of such 
copies, during the times therein mentioned, and extending the be- 
nefits thereof to the arts of designing, engraving, and etching his- 
ttrical and otjxer prints." 

THERON RUDD, 
Clerk of the Southern District of Nerv-York. 



> 



< ? 



INTRODUCTION. 



Amidst the pursuits of business, and the bus- 
tle of life, there are few men who are unwilling 
to give some moments to the gratification of cu- 
riosity, and the attainment of liberal information. 
The general diffusion of knowledge is guch, that 
a man would blush to be found totally ignorant 
of every thing, except the particular business in 
which the cares of life engage him. Who would 
be ignorant in geography, like the Spaniard of 
Monte Viedo, who asked in how many days 
he could ride to England ; or as the Hottentot, 
who went upon the mountain to lay hold of the 
moon by her horns, and bring her down ? In 
this age of mechanical invention, who would be 
unacquainted with the first principles of Mecha- 
nics, which never vary ? Amongst the Greeks, 



17 INTRODUCTION. 

it was thought shameful for a person to be igno- 
rant of the properties of the triangle, square and 
circle; yet what use could that simple people have 
for such knowledge, compared with the present 
generations. The pursuit of money is now the 
universal passioa, and human knowledge esteemed 
nearly in proportion as it conduces to the attain- 
ments of it ; yet there are many sublime truths, 
which, though not immediately profitable to the 
man of business, have a value of a different and 
more important kind. Such are all the sublime 
truths of Natural Philosophy or Physics, and of 
Astronomy : these lead us to a view of the whole 
system of the universe, and to connect with it the 
little globe which is our present habitation : these 
lead us in a particular and especial manner, to 
turn towards its author with humble and grateful 
hearts. 

The career of Chemistry has opened a wide 
field of information, and the progress of minute 
philosophy connecting itself with the arts of life, 
has been truly astonishing. The great system 
of the universe was demonstrated by Newton. 
The earth was connected by the law of gravita- 



INTRODUCTION* V 

tion with the heavenly bodies, but more particu- 
larly with the sun and moon, by whose influence 
the ocean is agitated, and the tides produced. 

Of late years, however, the mode of explain- 
ing this phenomenon, has been very justly ques- 
tioned, and for this reason ; namely, that the phe- 
nomenon or effect, does not agree icita the cause 
assigned. 

i 

The author having traversed the torrid zone, 
has had occasions to observe all the various mo- 
difications of which the ocean is susceptible, from 
the influence of the sun and moon, and has thence 
deduced (as he believes) the true theory or ex- 
planation of the ebbing and flowing of the sea, 
which he offers to the curiosity of mankind. 

The observations which he has been enabled 
to make in other parts of the world, all tend to 
confirm this new mode of explanation, and he is 
still in pursuit of others for the same purpose. 
He invites the inquisitive to confirm or to refute it 
with candor and impartiality. 



Vlll INTRODUCTION. 

of explaining that phenomenon, will confirm in a 
most remarkable manner, the general doctrine of 
gravitation; as established by Sir Isaac Newton. 

After meditating upon this subject for more 
than ten years, I find myself at length compelled 
to lay the result before the world. The objec- 
tions to the Newtonian account of the tide, stated 
by Sullivan, St. Pierre and others, but more es- 
pecially the disagreement betwixt the theory and 
actual phenomenon, first led me to think seriously 
upon it. I now deliver these thoughts, which 
are the result, to the world, believing them to be 
true ; if they are otherwise, let those who are able 
point out their falsehood ; as for those who are 
not able, let them be silent. 

The praise or censure of common critics can 
have but little influence on questions of this na- 
ture. I am well aware Ijefore what awful judges 
I stand. Let them measure out justice by the 
standard of truth, their mercy is out of the ques- 
tion. 

New-York, March iQth, 1816, 



THE 



EBBING AND FJLOWING- 



OF 



THE SEA, #* 



CHAP. L 

CONTAINS SOME PRELIMINARY MATTERS. 

i. Most of our first ideas want correction. It 
is somewhere said, that the ancients believed the 
sea was made to rise and fall, by the respiration 
of a great fish; this was well enough for the 
poets : nor was there a much better idea on the 
subject, as far as I can find, for many ages. What 
account Aristotle, who accounted for every thing, 
gave of the matter, I cannot tell, nor shall I go 
out of my way to inquire. 

B 



10 THE EBBING AND FLOWING 

3. It was discovered that the rising of the wa- 
ters of the sea accompanied the moon, and it was 
necessarily inferred, that she must somehow or 
other be the cause. Kepler was the first, I be- 
lieve, who gave any thing like a rational conjec- 
ture about the tides, asserting that the moou gave 
an impulse in her presence, which impulse pro- 
duced by its reaction, another in her absence. I 
do not find that this idea was followed by Kep- 
ler, so as in a satisfactory manner to account for 
all the various appearances of the phenomenon. 
Then came Newton, who demonstrated every 
thing in so subtile and profound a way, that if he 
committed any error, it was equally hidden from 
himself, and all who have since followed him. 

3. It may not be amiss in this place, to say 
something concerning the method of mathemati- 
cians, and the certainty of their conclusions. They 
begin with a few well known principles under the 
name of axioms ; and by the help of these, others 
are inferred, which were before unknown, and so 
on from one inference to another, never using 
any thing but what was at first self-evident, or 
since by their help proved to be true, or conform- 



OF THE SEA. il 

able to those self-evident principles or axioms, 
or somehow or other growing as a necessary con- 
sequence out of them : by this precise and care- 
ful method, this mode of proceeding has been 
dignified with the name of demonstrative science, 
and that most deservedly, since no other branch 
of human knowledge admits of a like degree of 
certainty; and as the mathematical sciences enter 
into, and as it were, lay the very foundation of all 
the important arts of life, they have always been, 
and no doubt always will be, entitled to the high- 
est consideration of mankind. 

4. It has, however, been objected by some, that 
the mathematical sciences are imperfect, because 
the mathematician can proceed just as well upon 
false data as upon true, and this is certainly the 
ease ; but it may be doubted whether this is an 
imperfection, and not rather the greatest perfec- 
tion his art can have, his business being only to 
deduce consequences from self evident principles. 
It is no fault of the art, then, that wrong conse- 
quences should be deduced from wrong princi- 
ples, which ought not to have been assumed ; the 
only care to be taken is, that no data be assumed 



12 THE EBBING AND FLOWING 

which is not true. Suppose, for example, I was 
to say for data, that 2 and 2, instead of making % 
make 5, thus : 2 + 2 == 5. Now nothing hinders me 
from working this equation just as if it were true. 
Suppose I would add 6 to both sides, then it will 
stand thus: 2 + 2+6 = 5 + 6, or 10 = 11. If I 
would multiply this last equation, suppose by 20, 
then 200 = 220; and so on through any number 
of operations. 

It may be seen that the error is, in this last 
equation, twenty times greater than in the first ; 
and if the operation be reversed, dividing by 20, 
the second equation will be produced 10 = 11; 
and subtracting 6 from each side, then 4 may be 
inferred to be equal to 5, agreeably to the false 
supposition. There is no fault here in the art 
itself, for it proceeded correctly upon the suppo- 
sition. We must be careful to suppose nothing 
but what is true ; and then we may rely upon all 
the deductions which we fairly make upon it. If 
I say that any quantity represented by a is equal 
to two other quantities represented by b and c, or 
a = b + c, then however I may increase or dimin- 
ish one side of the equation, if I do the same by 



OF THE SEA. 13 

the other, I shall never destroy it, or ran the 
smallest risk of drawing a false conclusion* 

But if there should happen to be an error in 
the supposition itself, namely, that a = b + c, and 
this error should be of such a nature that all man- 
kind fall into it, it would seem very difficult to 
correct it ; because, being in the data itself, and 
that data being false, and yet universally admit- 
ted as true, how is it possible in such a case to 
find out the error ? It can only be done by think- 
ing differently from all mankind, which is a task 
in itself infinitely difficult. 

5. If we would detect any error in the whole 
body of the mathematics, or mathematical philo- 
sophy, we must expect it only in the principles 
or data, for it is upon these the whole superstruc- 
ture is raised ; and this may appear to be correct 
and fair, although some error may exist in the 
data or first principles. And the same observation 
applies to the laws of motion, and to the rules of 
reasoning or philosophizing, as they are called,- 
which I shall here set down, because we must 
have an eye to them constantly in the following 



14? THE EBBING AND FLOWING 

inquiry. I shall shew hereafter, that a false 
supposition with respect to the moon's power of 
of attraction, led Sir I. Newton to adopt the 
theory which he left of the tides, and which 
misled him and all who have followed him upon 
that subject 

6. The first rule is — Not to admit more causes 
of natural things, than such as are true, and suf- 
ficient for explaining their phenomena, 

7. Rule %. Natural effects of the same kind, 
have the same causes. 

8 ? Observations on the foregoing rules. 

There is some danger of leaving out efficient 
causes, by a desire to account, according to the 
first rule, for a given phenomenon, by the agency 
of one cause, or following the rule by the fewest 
possible. We ought not to attempt to account 
for any natural phenomenon by the agency of one 
cause, if more than one equally claim to be admit- 
ted. Two causes can always produce a given ef» 
feet more easily than one singly; and if one of 



OF THE SEA. IB 

them can he shewn to be insufficient to produce 
the effect, the other, or some other, must be ad- 
mitted. 

An effect may result from one or more causes, 
and it is of the greatest consequence to distin- 
guish whether the cause is single or compound. 
A single cause, on the contrary, can never pro- 
duee but one effect, and that effect will be uni- 
form and proportionable to the cause ; if the cause 
varies, the effect will vary with it, and in the 
same proportion. 

Moreover, the manner of acting must not be 
overlooked, since motion may be produced in 
bodies more easily in one direction than in ano- 
ther; thus it requires less force to move a body 
sideways, than to lift it up perpendicularly ; and 
this truth will appear presently to be of the 
greatest consequence. 

It may yet further be observed, with regard to 
cause and effect, that the true cause will ever be 
just, adequate, and proportionable to the ef- 
fect and no more ; in any case, if a disagreement 



i& THE EBBING AND FLOWING 

or incongruity can be shewn betwixt them, we 
may be sure the cause is not rightly assigned. 

9. The laws of motion are as follows : 

Law 1. All bodies conthme in a state of rest 
or of uniform motion in a right line, till made to 
change their state by some external force. 

Law 2. The change of motion is proportional 
to the force impressed, and that change is pro- 
duced in the same direction or right line in which 
the force acts. 

Law 3. Action and reaction are equal, but 
with opposite directions. 

It is said that all actions of bodies upon one 
another conform to these laws, and as far as we 
are acquainted with the actions of bodies on each 
other, they do do so ; but when we apply them to 
those actions of bodies upon one another, with 
which we are not acquainted, as gravity, then 
those laws become liable to objection ; as for ex- 
ample : in a body falling to the earth by its gra- 



OF THE SEA. 17 

vity, whether the impelling force be internal or 
external ; whether it resides in the earth, or in 
separated falling matter itself, no mortal man, I 
believe, can tell ; and further, if it resided in the 
earth, small bodies ought to fall with a greater 
celerity than largff ones, to preserve an equal 
momentum* according to the ordinary mechanical 
powers, with which, however, the law of gravity 
seems to have no connexion. 

I 10. But to return to our subject : I shall con- 
clude this preliminary chapter, by giving a table 
of the rise of the waters of the sea, by the joint 
influence of the sun and moon at the full and 
change f and though I am sensible these observa- 
tions, taken from ordinary books of navigation, 
are not so exact as could be wished, yet they will 
serve my purpose, as I intend only to use them 
in a general way. 

I have selected only a few places on each shore 

of the Atlantic Ocean, and those as much out of 

the influence of local circumstances as I could. 

In this respect it is to be wished that they were 

still more so. 

C 



THE EBBING AND FLOWING 



A TABLE, 

Shewing the perpendicular rise of the tide at the 
undermentioned places, with the hour at Full 
and change of the Moon. 



Halifax and Nova" 


F. 


H. 


M. 


Sctitia generally I 


£ 8 


7 


**0 


Boston, 


12 


11 


30 


New- York, 


5 


8 


54 


Rhode Island, 


5 


7 


37 


Bermuda, 


5 


7 





Charleston, 


6 


7 





Jamaica, 1 or 1 2 in. 






Mouth of the A-n 








mazon River, \ 


* * 






under the line, J 









p. 


H. 


,r. 


6 


10 


30 


5 






8 


10 


30 



11 



Shetland rises 
North end only 
The Orkneys, 
The west Coast" 

of Ireland, 
Coast of Portugal, 10 2 30 
Madeira, 7 12 4 

Port Pray a, Cape^># 

de Verdes, j 
Cape St. Mary, \ 

nearthemouth( 2 , JQ ^ 

of the River ( 

Gambia, J 

Bight of Benin,zw% 

the rivers 6 feet > 4 & 5 

but out at sea ) 



* No tide at the mouth of the Mississippi, nor generally in the 
upper part of the Gulf of Mexico, consequently there cannot be 
?nucb at the mouths of the Oronoko and Amazon. 



OF THE SEA. i% 

The tides are better known on the coast of 
South America from the line southward; thus at 
Bahia and Rio de Janeiro, they are 4 and 5 feet; 
at the River Plate 6, and some say 7 — but at the 
Gape of Good Hope the rise is only from 3 to 5 
feet, according to the circumstances of variable 
winds. At the small islands of St. Helena, As* 
cension and Tristan de Cunha, there is very lit- 
tle tide. At the Falkland Islands 6 or 7 feet 

According as local circumstances vary, so tviU 
the tide vary in different places ; thus out in the 
ocean the tides come on sooner, and do not rise 
so high as at places where by the formation of 
the land, the water is accumulated and pent up, 
as in the Bristol Channel, and the Bay of Biscay, 
where it accumulates so much as to rise to an 
extraordinary height ; all these local circumstan- 
ces I wish to avoid as much as possible, and en- 
deavor to discover some general principles for 
the ocean itself. 

41. Now in casting one's eyes over the fore- 
going little table it appears, first, that the tides 
rise higher in tha temperate than in the torrid 



SO THE EBBING AND FLOWING 

zone, contrary to the present theory of the tides ; 
secondly, that the tides do not appear to rise so 
high on the shore of America as on that of Europe 
and Africa; thirdly, that the hour of high water 
appears to be different, and generally later on 
the American shores, even at places but little in- 
fluenced by local circumstances. 

The following observations are from Captain 
Cook's third voyage, and from Bligh's voyage to 
the South Sea. 

FRIENDLY ISLES. 

*f At these islands the tides are more consider- 
able than at any other of Capt Cook's discove- 
ries in this ocean, that are situated within either 
of the tropics." " In the channels between the 
islands, it flows near tide and half tide ; and it is 
only here and in a few places near the shore that 
the tide is perceptible, so that we could only 
guess at the quarter from whence the flood comes. 
At Annamooka it is high water near 6 o'clock, 
on the full and change of the moon, and the tide 
rises and falls about 6 feet. At Tongataboo the 



OF THE SEA. 31 

tide rises and falls 4 feet three quarters on full 
and change days, and three feet and a half at the 
quadratures." 

Lat. of Annamooka, 20, 15, S. 
Tongataboo, 81, 8. 

At Matavia, Otaheite, the tide seldom exceeds 
10 or IS inches, lat. 17, 29, S. 

At Port Jackson, 6 feet spring and 4 feet 6 
inches neap. 

Pelew Islands 8 or 9 feet; currents are always 
found near the shore. 

At the village of St. Peter and St. Paul, Kamt- 
schatka, lat. 53, 38, full and change, high water 
4h. 36m. rise 5 feet 8 inches. 

In the island of Onalaska, about the lat. 53, 30, 
the tides are said to be " not very considerable, 
except in Cook's River f 9 to the northward of 
Cape Prince of Wales, neither tides nor currents 
were observed. CooWs Voyages. 



23 THE BBBING AND FLOWING 

False Bay, Cape of Good Hope. The time of 
high water is three quarters past 2 on full and 
change days, and the tide flows about 6 feet. 

Vandeiman's land, lat. 43, 31, high water 49m. 
past 6 in the morning, at the change of the moon 
rises 2 feet 6 inches. 

Bligh's Voyages to the South Sea. 

This is a sketch of the phenomenon ; we will 
mow proceed to inquire into the cause or causes, 
as also their mode or manner of acting. 



O? THE SEA* 23 



CHAR II. 

OF THE THEORY OF THE TIDES, AS IT STANDS AT 
PKESENT, AND ITS REFUTATION. 

1. That principle, whatever it be, by which 
bodies fall towards the earth is called gravity, 
and is found to extend to the sun, moon and 
stars ; in a word, to be universal throughout the 
universe. It is this which preserves the rotun- 
dity and compactness of the earth ; that keeps 
every thing in its place, and without which the 
world could not exist. 

2. All bodies contain more or less of matter, 
and a small body may have more matter than a 
large one, on account of its parts or particles be- 
ing more closely united ; it is the quantity of its 
matter which constitutes its weight, and weight is 
only another name for gravity ; so that all bodies 
gravitate according to their weight or quantity of 
matter; for every particle is alike indued with 
this property, and the gravity of the whole is no 
more than the sum of the gravity of the parts. 



21} THE EBBING AND FLOWING 

For this reason also, a large or a small body 
falls with the same velocity ; for the large one (as 
a ton) is made up of small ones (as ounces) and 
every ounce is alike indued with the gravitating 
principle, and so the ton and the ounce fall 
equally fast, provided they fall from the same 
place or distance from the earth* 

But if one of two equal bodies is supposed to 
be farther from the earth than the other, in that 
case they will not fall with the same velocity, but 
the nearest to the earth will fall fastest, and the 
more remote the other is, the slower will it fall. 

3. Now it has been discovered and proved, 
that the principle of gravitation observes a parti- 
cular law at a|J distances, which is so constant 
and so true, that it well deserves to be called a 
law of nature ; which is, that as a body is remov- 
ed from that towards which it gravitates, its gra- 
vity or weight diminishes ; not as the distance, 
but as the square of the distance, so at different 
distances it is inversely as the squares of those 
distances. 



OF THE SEA. 35 

4. It will not suit the brevity of my design, 
to enter into the demonstration of established 
truths ; those who are in any manner acquainted 
with geometry will know this truth, and those 
who are not, must either take it upon trust, or 
refer themselves to elementary works upon such 
subjects. 

Gravity then diminishes ats the square of the 
distance increases, thus : suppose a particle of 
matter, or a drop of water, on the surface of the 
earth, gravitates in a certain small degree towards 
the moon, and another at the earth's centre gra- 
vitates also towards the moon ; if we would com- 
pare the force of gravity at these two places toge- 
ther, we must square those two distances, and 
then take them inversely ; that is, the square of 
the greater distance Will express the gravity of 
a particle at the surface, and the square of the 
least will express the gravity of a particle at the 
centre of the earth, both considered as gravitating 
at those places respectively towards the moon ; or 
rather, it is the ratio of these respective gravities 
which is expressed by the squares of the dis- 
tances taken inversely. 

D 



gO THE EBBING AND FLOWING 

Now as the moon's distance from the earth is 
only 69 semi-diameters of the earth, a particle at 
the earth's surface under the moon will be only 59 
of those semi-diameters, and a particle on the op- 
posite side will be 61 ; the squares of which num- 
bers will differ considerably, and therefore the 
gravity of a particle of matter, or a drop of water 
on the different surfaces, and at the centre of the 
earth towards tha moon, will differ considerably ; 
and it is upon these differences that the present 
theory of the tides is founded, and I wish the reader 
to be very particular in attending to this point. 

Let us now consider the same particles of mat- 
ter as gravitating towards the sun. The sun's 
distance being so immensely great, compared to 
that of the moon, that although the gravity of any 
particle of matter, or drop of water on the earth's 
surface, is much greater towards the sun, than it 
is towards the moon, yet the ratio of the square^ 
of the Instances at the surface of the earth, nearest 
the sun, at the centre, and at the farthest surface, 
taken inversely, is much less than in the case of 
the moon ; for, suppose the sun's distance to be 95 
w 96 millions of miles, the addition or subtrac- 



OF THE SEA. 2/ 

tionof the earth's semi. diameter will leave the 
number so near what it was, that the difference 
of the squares will be almost nothing. 

If we consider the sun's distance in semi-dia- 
meters of the earth, it will be in round number 
about 24,000 of such semi-diameters, and it is 
evident that the addition and subtraction of the 
nniuber 1, will give 3 numbers for the respective 
distances of the farthest surface, the centre, and 
nearest surface of the earth, the ratio of whose 
squares will differ less than the ratio of the 
squares of 59, 60 and 61 ; and so the difference be- 
tween the gravitation of matter at the centre, far- 
thest, and nearest surfaces of the earth is greater 
in the case of the moon, than in the case of the 
gun, although the gravitation itself is much greater 
towards the sun than it is towards the moon. 

5. If we apply this principle to the waters of 
the ocean, we are told the whole phenomena of 
the tides will be explained by it. 

Although I mean to combat the present theory, 
yet I wish to state the principle as clearly and 



38 THE EBBING AND FLOWING 

as distinctly as I can, and also the manner of its 
application for explaining the ebbing and flow- 
ing of the sea, and therefore I shall proceed to 
shew how this difference of gravitation at the 
centre, and at the surface, is made use of for that 
purpose. 

Philosophers, observing that the moon goes 
round the earth as her centre, and the earth 
' round the sun as her centre, and as the principle 
of gravitation is reciprocal and universal, the earth 
may be considered, they say, as going round the 
moon, or rather round the common centre of gra- 
vity of the eayth and moon evei^ lunation. Now 
this common centre of gravity will be so much 
nearer to the earth, than to the moon, as the matter 
in the earth is greater than the matter in the 
laoon, which is considered to be as 40 to 1, and so 
the common centre of gravity of these two bodies 
is 40 times nearer to the earth than it is to the 
moon, 

In common mechanics, when we speak of a 
common centre of gravity, it means when applied 
to two or more bodies any how connected, that 



OF THE SEA. 29 

point which heing suspended, the bodies them- 
selves will be suspended. 

Suppose now the earth and moon so connected 
together, that like two weights on a steelyard, if 
the fulcrum or point of support be suspended, 
both the earth and the moon would be suspended 
in equilibrio ; this is the common centre of gra- 
vity of which I am speaking. 

It may be easily found thus ; since the matter 
in the earth is 40 times more than the matter in 
the moon, the common centre of gravity will be 
40 times nearer the earth than to the moon, as 
was said above, therefore to produce an equation, 
we have only to multiply matter and distance on 
each side of the fulcrum or common centre of 
gravity. 

Let the distance of this point from the centre of 
the earth in miles be called x, then will the distance 
of the same point from the moon be 240 000 — x. 
Now call the matter in the moon I, then the mat- 
ter in the earth will be 40 ; multiplying distance 
and matter on both sides, you will have 



80 THE KEBIN© AND FLOWING 

40 07 = 240 000 — x and 

transposing, 41 x = 240.000 dividing both 

it ,, 240.000 „ KO , . ., 

sides by 41 x = — : = 0853 + in miles. 

J 41 

Thus then the place of this common centre of 

gravity, so important in this problem of the tides, 

is situate a little without the earth's surface, her 

seini-diamcter 4000 miles being subtracted, leaves 

only 1853 + . 

6. The earth goes round in this little circle 
every lunar month, in order to balance the moon ; 
by the law of gravitation, that is a very little 
circle in a very long time. If we compare this 
motion or velocity with others in the system, it 
will scarcely deserve the name of motion : thus 
the earth, in turning round on its axis every 24 
hours, any place under or near the equator, goes 
move than 1000 miles an hour, and going in her 
annual orbit more than 60,000 miles every hour. 

Now this common centre of gravity being dis- 
tant from the centre of the earth only 5853 miles, 
the whole diameter is 11,706, and the whole cir- 
cumference 36,000, near enough for our purpose, 



OF THE SEA. 31 

and so the motion hourly is about 55 miles ; a mo- 
tion which, compared with others, as I said be- 
fore, scarcely deserves the name. 

7. However, philosophers have inferred, that 
as the earth goes round in this little circle, she 
is continually falling from the tangent of the 
same little circle or orbit; and also they say, 
that if the earth was left to fall freely towards 
the moon, in that case the matter of the earth 
gravitating according to the general law before 
mentioned, that is to say, inversely, as the 
squares of the distances, the parts of the earth 
nearest the%neon gravitating mare than the cen- 
tre, and the parts farthest from the moon gravi- 
tating less than the centre, there will necessarily 
arise an elongation on the earth's surface in the 
fall, the parts nearest to the moon advancing 
more rapidly than the centre, and the paris oppo- 
site or farthest from the moon hanging behind, and 
from hence say they, there will result a tide 
both on the side next or under the moon, and on 
the opposite or farthest side at the same time; 
and as the earth turns round on her axis in 2£ 
hours, all places on the earth will come in sue- 



32 THE EBBING AND FLOWING * 

cession under the moon, and so at all placet 
there will be a tide twice in 24 hours. 

8. But the philosophers go on to say further, 
that not only if the earth was left to fall freely 
towards the moon, such an effect would ensue, 
but also if she does not fall, yet the same cause 
which would produce the effect if she did fall, 
will still produce the effect if she falls not at all. 
This doctrine is far above my comprehension. 

How an effect can equally ensue, whether 
there is cause or no cause, I have yet to learn. 
It does not seem to me to be sou/Id doctrine. 
How can a body be said to fall, which does not 
approach that towards which it is falling? And 
unless there is an actual failing, an actual ap~ 
proachj' the difference produced by the law of 
gravitation cannot take place, fbecause it depends 
upon that actual falling or actual approach for 
its cause, )and if there is no cause, how can there 
be an effect? How can an effect which is said to 
have falling for its cause, equally take place, 
when there is no falling or no cause P However, 
let us forbear a little and go an. 



OF THE SEA. 83 

9. The same thing is said with respect to the 
sun as to the moon ; the earth is considered as 
falling from the tangent of her annual orbit, and 
her parts gravitating in the fall, according to the 
general law above stated, the same effect will 
be produced from the same cause, only in a less 
degree, for the reasons above mentioned. Com- 
bining together these different gravitations, as 
they conspire at the conjunction and opposition 
of the moon, and as they retard and hinder, and 
cross at the quadratures, the whole phenomena 
of the tides has been explained. 

10. 1 hope it will be allowed that I have 
stated the thing fairly, because, as I presently 
mean to begin to knock it all down again, I wish 
very much to shew first, that I know what I am 
about, at least, what it is that I undertake. 

11. In order to be consistent, the philosophers 
were obliged to say, that in the equatorial re- 
gions, being the place where the particles on the 
earth's surface, were most subjected to the dif- 
ference of gravitation so often mentioned, the 

tides would be most sensible, or highest, the lit-' 

E 



M THE EBBING AND FLOWING 

tie table of tides in the 1st chapter shews the con- 
trary, of which, more by and by. 

One error begets another ; all the calculators 
take care to inform us, that their calculations are 
for the equator ; some of them make the tides 
rise there 11 or IS feet; some 8 or 9 — some 
more — some less — why they disagree, is no bu- 
siness of mine. But this I can say to them all — 
you are all mistaken — you have left nature, and 
bewildered yourselves and others with your flux- 
ionary calculations, and how to make them con- 
form to a theory which has no other foundation 
but your imaginations. 

The tides in the torrid zone are not more than 
half what the calculators make them ; and the 
half of this half,- it is probable, is produced by 
the resistance of the land, against which the wa- 
ters of the ocean run, so that what fairly belongs 
to the luminaries of heaven, is only one fourth of 
what has been assigned to them by the philoso- 
phers ; they say, indeed, that there must be room 
fpr the luminaries to act, and the ocean being 
narrower in the torrid zone, than in the tempe- 



OF THE SEA. 35 

rate, the tides on this account will be less. One 
does not very well see the necessity for so much 
room upon the principle of direct gravitation, of 
which so much has been said ; but we will give 
them as much room as they like. Let them go 
into the Pacific Ocean, or let them sit where they 
are, and look into the little table of tides, what 
account Captain Cook and others give of the 
tides in that vast ocean, 

u Hence it appears," says Mr. Maclaurin, in 
his account of Sir Isaac Newton's discoveries, 
" that it is only in the great oceans that such 
tides can be produced, and why in the larger Pa- 
cific Ocean, they exceed tnose in the Atlantic 
Ocean." That great mathematician must have 
been very confident in his theory, when he ha- 
zarded such an assertion without proof. 

They must have room they say ; let them have 
it ; in the latitude of Charleston and Madeira, 
the ocean is much wider than it is in the latitude 
of Ireland and Nova Scotia, yet the tides are 
much less. 



36 • THE EBBING AND FLOWING 

12. I am now to make my stand against this 
falling doctrine, which I do upon the four fol- 
lowing reasons. 

Reason i$t. There is no such thing as the 
earth falling toward the moon ; a falling supposes 
the body to be first at a greater distance, and 
after the fall at a less distance, whereas the earth 
keeps at the same distance, and therefore does 
not fall. 

I deny that she falls from the tangent ; she is 
never in the tangent, but always in the curve. 

Ileas n 2d. Supposing there was a falling, in 
the way the philosophers say, they will gain no- 
thing by it, as I will shew them. 

Suppose then, the earth was to fall freely to- 
wards the moon, would the parts of the earth 
begin presently to separate ? surely not, unless 
the gravitation of its parts towards itself was 
suspended or destroyed ; for all the way down 
the fall to the very stroke of impingement, the 



OF THE SEA. 37 

matter in the earth will still be 40 times greater 
than that in the moon, and therefore a particle 
on the earth's surface would not forsake a greater 
to obey a less force ; for to say that a less force 
can overcome a greater, is not allowable. 

If then, in any part of such a fall, the mutual 
gravitation in the parts of the earth remaining, 
no such separation of the parts *f the earth could 
take place, much less would such a separation 
take place in the very first moment of beginning 
to fall. 

Let us compare the gravitation of a particle 
of matter on the earth's surface; 1st. towards 
the earth itself; Sdly. towards the moon; and 
3dly. towards the sun. 

Call the semi-diameter of the earth i ; call also 
the matter in the earth 1 ; then the gravitation of a 
particle of matter on the earth's surface will be 4. or 
1. Now, as the distance of the moon from the same 
particle, at a mean rate, is 60 semi- diameters of 
the earth, and the matter in the moon only A of the 
matter in the earth, the expression for the moon 



38 THE EBBING AND FLOWING 



will be — ^ or ~ — 



—2 m 60 x 60 "" 60 x 60 x 40 "" 144.000 

60 

lastly, the distance from the sun of the same par- 
tide on the earth's surface, may be taken in a 
round number at 34.000 of the same semi diame- 
ters (for we must preserve the same measure in 
all the cases) and the matter in the sun being 
taken, as it is usually taken, at 169,£8& times 
that in the ear*, then the expression for the 
gravity of a particle of matter on the earth's 

169.282 

surface towards the sun, will be 2 or 

24.000 

169 .382 169.2S3 1 

84.000 x 24.000' ° r 576.000.000' ° V 3400' near ' 

ly ; thus we see that when the gravity of a parti- 
cle on the earth's surface is considered as unity, 
the gravitation of the same towards the sun, is 
only a 3400th part of unity, and towards the 
moon, only 144,000th part of unity. 

Now then, if the earth was actu^ly falling to- 
wards the moon, could any body reasonably as- 
sert, that her own power of 1 would be over- 
come by a power of tttt^t: ? It might just as 
144.000 



OF THE SEA. 39 

well be asserted, that a person exerting the force 
of one pound to lift up a ton, would therefore 
lift it. I have never yet met with an instance of 
any thing being lifted up, unless a force at least 
greater than the thing to be lifted was exerted. If 
the earth was to fall freely towards the sun, the 
parts of the earth in this case would separate, by 
the law of gravitation, but not till the earth had 
travelled many million of miles, and her own 
gravitation was overpowered by the sun's greater 
force. 

Why the moon has more power to raise the 
waters of the sea, or rather, why the tides follow 
the moon more than the sun, will appear in its 
proper place. 

Reason 3d. If falling was the cause, or was 
necessary to produce by the law of gravitation, ar 
a separation or a tendency to separation of the 
parts of the, earth, both before and behind, the 
earth, at the time of full moon, would be placed 
in the awkward predicament of haviug to fall 
contrary ways at the same time ; towards the 
moon, to produce the lunar tide, and toward* the 



40 THE EBBING AND PLOWING 

sun, to produce the solar tide; a thing not to be 
understood. 

Meason ^th. If the foregoing reasons were no 
reasons at all, yet this fourth would of itself be 
abundantly sufficient to prove, that the true cause 
of the tides is not rightly assigned; for if it was, 
the tides would necessarily be highest at and 
near the equator, or that part of the torrid zone 
to which the sun and moon are vertical, and de- 
cline towards the poles, whereas they are high- 
est near the middle of the temperate zones, and 
decline as we approach the equator ; they de- 
cline also from the temperate zones towards 
the poles. 

Now if an effect does not correspond and agree 
with the cause assigned, are we not to conclude 
most certainly, and positively, that the cause so 
assigned, is not the true cause ? 

I might here add for another reason, if it was 
necessary, that if there was an actual falling of 
the earth towards the moon, the further surface 
of the earth would be most of all attracted, or 



OP THE SEA. 41 

more correctly, would gravitate more in the di- 
rection of the moon than any other part of the 
earth ; for it would gravitate in that line, at once 
towards the moon, and towards the earth, and its 
gravitation would amount to the sum of both. 
Now it would be very singular indeed, if those 
very particles so situate should lag behind ; for 
to say that they would, would be to say that these 
very particles gravitating more than any other in 
that direction, that is, in the direction of the fallj 
yet turn sulky and will not come up so fast as 
others which are actuated by a less force ; in a 
word, it would be to say, that the greater is not 
the greater; that a greater cause produces a less 
effect than a less cause, and so on. 

Again, once more ; supposing the earth was in 
a state of actual falling towards the moon, the 
centre of the earth would be influenced in that 
direction by the moon only, but the farther sur- 
face would be actuated in the same direction by 
the moon marly as much as the centre, and by 
the whole body of the earth into the bargain ; 
which, as has been shewn, is 144,000 times 

greater than the other, and yet we are required 

F 



4$ THE EBBING AND FLOWING 

to believe that those very particles will still not 
keep up. 

If the reader is not incorrigibly obstinate, al- 
though all my reasons should fail to convince 
him of the fallacy of the present system of the 
tides, built upon the falling argument, yet if he 
will take the trouble to read the next chapter, he 
may find other collateral reasons for abjuring his 
error, however strongly and deeply it may have 
taken root in his mind. 



OF THE SEA. 43 



CHAP. III. 

CONTAINS AN ENTIRELY NEW EXPLANATION OF 
THE TIDES. 

1. Having in the last chapter pulled down the 
fabric, and scattered about the materials, they 
must not however be lost, since they will serve, 
with a different disposition, to build it up again 
anew, in a manner more simple, more elegant, 
more noble, with juster proportions in its parts. 

In order not to build upon the quicksands of 
fancy and imagination, I will lay the foundation 
upon the solid rock of experiment. 

2. There are many things which seem ex* 
tremely simple and easy in themselves, which 
yet upon further inquiry, produce insurmountable 
difficulties. 

An instance may be this : suppose you are sit- 
ting sociably with your family and friends, and 
some one should say, this is a very beautiful 



44 THE EBBING AND PLOWING 

table, but it is square, and I do not admire square 
tables. It was on that verv ace unt that I chose 
it, because I know we have the same room en 
all sides. Yes, yes, that may be very well, ut 
you never can know how far it is from one cor- 
ner to the opposite corner, in the same measure 
as the sides, and that is my objection to (square 
tables. Very strange, indeed, if I cannot, since 
I can measure it in a moment ! Very well, do 
so ; the side is exactly 6 feet 2 inches, and the 
diagonal is — how much ? Now if all the men in 
the world, were to calculate from the beginning 
of the world to the end of it, they never could an- 
swer this question, simple as it might at first seem. 

Another question may seem infinitely compli- 
cated and abstruse, and yet may turn out to be 
the simplest and most obvious, and easy, and 
most natural thing in the world, and such is the 
genuine theory of the tides. 

DEFINITIONS. 

3. I distinguish between direct gravitation and 
lateral gravitation of matter on the earth's sur- 
face, towards the sun and moon. 



OF THE SEA. 45 

Definition 1. Direct gravitation is that which 
takes place when the sun or moon are in the 
zenith of any place upon the earth's surface, and 
is in the same line that any particle of matter 
on the earth's surface gravitates towards the 
earth's centre. 

Definition 2. Lateral gravitation, I call that 
which takes place at 90 degrees distance from 
the former, or when the line of gravitation of a 
particle of matter, or drop of water on the earth's 
surface towards the sun or moon, is at right an- 
gles with the line of its gravitation towards the 
earth's centre. 

EXPERIMENT I. 

Fig. 1. Suspend a weight W, the larger the 
better; but suppose one ton, at the end of a chord 
A B, the longer the better, but suppose 100 feet ; 
now suppose a person should lift at A with the 
the force of one ounce or one pound, he will not 
lift the weight in the smallest degree, yet it is 
very true, that if the weight W was weighed in 
scales whilst this force of one ounce or one pound 



46 THE EBBIN& AND FLOWING 

was exerted, tbe weight W, would weigh one 
ounce or one pound less than it did before such 
force acted upon it at A. Now this force at A, 
acts in the line of direct gravitation, see Def. I. 
Observe yet more : not only will the force of one 
ounce or one pound, exerted at A in the line of 
direct gravitation, be unable to raise the weight 
W in any the smallest degree whatever, but it 
will be unable to give any kind of motion what- 
ever to the said weight W. Let the force be ex- 
erted at a, at 6, at c, and so on down to/. Now 
it is obvious, that whatever power it has to move 
the weight at a, it will have more at b 9 still more 
at e, and so on down to g 9 where it will have the 
greatest power of all to move the weight W, in 
the line of lateral gravitation W g. 

This we see exemplified every day in drawing 
goods by a crane, to the different floors or stories 
of a warehouse, which here may be represented 
by the letters a, 6, c, d, e and/. The least force 
even of a child will draw the weight W, however 
great, into the lowest floor /, but the strongest 
man, whilst it remains in that position, cannot 
draw it into any of the other floors, and the 



OF THE SEA. 47 

higher he aseends, the less power he will have, 
to give any motion whatever to the weight W, and 
in the direction A B, he can give no motion at 
all to it. 

EXPERIMENT IL 

Let a wheel, no matter how large and heavy, 
be suspended on its axle-tree from the ground, 
as is done in all cases when wheels are put on, 
or taken off; whilst thus suspended, the least 
touch of the finger on the rim, if exerted in 
the plane of the wheel, and in a line perpen^ 
dicular to any radii or spoke of the wheel, will 
put it in motion, whilst it would take the force of 
the strongest man so to lift the wheel, as to take 
its gravity from the axle. tree. 

EXPERIMENT III. 

Suppose you have a walking-stick which 
weighs one pound, or 5760 grains, or 11,520 half 
grains; take the same and balance it upright 
upon the floor, or if you cannot do it, conceive it 
to be done, (Fig. 3.) Now one of these 11,520 



48 THE EBBING AND FLOWING 

half grains, exerting its force in the direction a &, 
will give motion to the head of the stick in that 
direction, but the whole of them, 11,520, cannot 
give the least motion whatever to the stick, if 
their force is exerted in the direction a c, perpen- 
dicular to the horizon. 

In a ton, there are 2240 pounds, or 4480 half 
pounds-*— in experiment 1. One of these half 
pounds will give some motion to the weight W, in 
the direction W g 9 but the whole 4480 cannot, if 
exerting their force in the direction W A, give 
any motion whatever to it. 

Of the same kind is the force which draws or 
urges boats or ships on the water, when exerted 
to give motion to these in a line parallel to the 
horizon ; but the same force, if exerted to lift 
them up or oat of the water, would produce no 
effect, or rather [no motion at all. 

A pendulum is of the same kind, and the wa- 
ters of the ocean may be considered as suspended 
like the ball of a pendulum, and as having a 
semi-diameter of the earth for its rod ; the ball of 



OF THE SEA. 49 

the pendulum being supposed to be suspended on 
the top, instead of hanging at the bottom of the 
rod, or the pendulum being considered as in- 
verted. 

4. We come now at last to apply this same 
principle to that motion which is produced in 
the waters of the ocean by the sun and moon, 
and from which motion the tides result, as their 
adequate and sufficient cause. 

Fig. 2, JVb. i. Let S be the sun, distant 
from E the earth, 24,000 semi-diameteis of the 
earth, and M the moon, distant 60 semi-diame- 
ters of the earth from it ; owing to the immense 
distance of the sun, there is no having a diagram 
with true proportions ; on this account I leave S 
out. but it may be easily conceived to be beyond 
M, with a distance of 400 times E M from E. 
In order to give a more distinct view, No. 2 is 
E enlarged. Now it is evident, that the greatest 
effect of the sun and moon upon the waters of 
the ocean, to put them in motion, will be at a, 
and the least at rf, where indeed it will be no- 
thing. The waters at a, being suspended as it 

G 



50 THE EBBING AND FLOWING 

were on a wheel, or at the end of a chord, whose 
length is a semidiameter of the earth, may easily 
be moved laterally, or in a line which is perpen- 
dicular to the line of their gravitation towards 
the centre of the earth, or a c; that is to say, 
may be easily moved in the direction a S, or a 
M, there being nothing to oppose such motion, 
but the vis inertia* of the waters themselves. 

The same thing may be said of the waters at O, 
where the same lateral action will take place, 
but in a contrary direction as respects the rota- 
tion of the earth on her axis ; so that there will 
be at every place, twice in 24 hours, an impulse, 
one of which drawing the waters to the shore, 
will make a tide, and another drawing the waters 
from the shore, an ebb, and the reaction of these 
will produce another tide and another ebb ; all 
this will appear more fully by and by. 

It is evident also, that the water at b, will not 
be moved so easily as those at a, and those at c, 
with still more difficulty, and those at d, or im- 
mediately under the luminary, not at all ; because 
being now iu the line of direct gravitation, the 



V 



OF THE SEA. ' 01 

proper gravity of the water towards the earth's 
centre will overpower the other, and so no effect 
will ensue as to motion. 

Again, it is evident by inspection, that the wa- 
ters continue to be lateral much longer to the 
moon than to the sun, from her lower position ; 
thus, a ray drawn from b to S, goes up to one of 
the upper floors, in experiment i, whilst a ray 
drawn from b to M, goes to a lower floor (though 
not the lowest) and it was shewn, that the lower 
any given force acted in the set of floors, the 
more power it would have, and the higher the 
less power it would have to produce motion in 
the weight ; in other words, the line b S ap- 
proaches nearer to the line of direct gravitation, 
and the line b M nearer to the line of lateral gra- 
vitation, which gives the moon an advantage at 
point 6, although her power is less. 

Even at c, the moon may continue to have 
some small influence, whilst the sun can have 
none. Now as the waters at a, will pass suc- 
cessively the places b and c, and so on to (?, it 
is evident that the sun and moon will have less 



; 



5% THE EEBING AND FLOWING 

and less power over them, till they arrive at the 
place A y where it will vanish altogether. 

The same thing may be said of the waters, at 
a?, y and z 9 as they arrive in succession into the 
situations of a, 6, c and d. 

Thus it appears, that the sun's action is much 
greater than that of the moon, but it is continued 
for a very short time ; the moon's action is less, 
but continued longer ; moreover, what the sun 
begins, the moon has the advantage of taking up 
and continuing ; and as it is well known that a 
much less force will continue a body in motion, 
than is requisite to put it in motion, hence, on a 
double account, the moon appears to have the 
greatest effect upon the waters of the ocean ; and 
as her action is last, the tides appear to be more 
the effect of the moon than of the sun, though in 
truth the sun's force is much greater ; and it will 
be shewn by and by, that even at the quadra- 
tures, the sun contributes, much to produce the 
tides ; and it may be questioned whether the 
moon, singly, and without the help of the sun 
to originate motion in the waters of the sea — it 



OF THE SEA. 53 

may be questioned, I say, whether the moon 
could produce any motion, and therefore any tides 
at all. 

5. I have pointed out the manner in which the 
least force, or a given force, can produce the 
greatest effect in giving motion to the waters of 
the ocean ; and as every thing in nature is pro- 
duced by the most simple law, or means, I think 
it follows, that this is the true way in which it is 
actually produced ; and if motion in the waters 
of the ocean is sufficient to produce tides, we 
have the simplest cause of that motion, and find- 
ing that to be sufficient, we have nothing more 
to seek. 

Now that this most simple of all modes of giv- 
ing motion to the waters of the ocean is sufficient 
to produce the tides, I will proceed to shew\ 

Motion in the w r aters of the sea being all that 
is wanted to produce tides, that manner of acting 
to produce motion, which can produce the great- 
est quantity, with the least force, must be the 
true manner of acting in nature ; for if the motion 



54 THE EBBING AND FLOWING 

was produced by any other mode of acting, yet 
this greatest and most powerful manner would 
remain, and then there would be two modes of 
producing it; a less, which is sufficient, and a 
greater, which did nothing, which is absurd j 
therefore this is the true way, and being sufficient, 
is the only one ; for u we are not to assign more 
causes to natural effects, than such as are true, 
and sufficient to explain the phenomenon " Rule 
1, page 14. 

6. Having now shewn that the motion of the 
waters of the ocean, from which the tides result, 
arises from a lateral and not from a direct gravi- 
tation, it is time to apply the same principle to 
explain the actual phenomenon, as we find it in 
nature. 

PROPOSITION I. 

To shew in what manner the tides on a western 
shore are produced. 

Case 1. Suppose it to be new moon. 



OF THE SEA. 55 

When the sun and moon come to, and have 
passed the eastern edge of the horizon of the 
shore (as for example, the western shore of Eu- 
rope) a gravitating motion will begin to take 
place toward them, at first scarcely perceptible ; 
but as it is continued every moment, it is evident 
that this motion will be an accelerated one, and 
therefore, it will become more and more rapid 
for some time. As the sun and moon acquire al- 
titude, more and more water will begin to move 
towards the shore; the sun will act most vigor- 
ously, but for a shorter time ; the moon with less 
force, but longer continued. The waters being 
thus put into motion, will run directly for the 
land ; and by the laws of motion, a body of any 
kind being put in motion, will continue in mo- 
tion till it is stopped by some external cause. It 
is evident enough in* this case, that the land 
will stop the water ; by which stoppage, how- 
ever, the water will be mounted up, which we 
call a tide. 

Besides the sun and moon, then there is ano- 
ther cause which contributes more or less to raise 
the waters upon the shores of the ocean, and to 



56 THE EBBING AND FLOWING 

produce a tide, namely, the land, against whicli 
the waters flow ; and this third cause, always 
considerable, is in very many instances, greater 
than the other two put together ; thus, the tides 
rise on the western coast of Ireland, 11 or IS 
feet only, but in the Bay of Biscay, in the Eng- 
lish Channel, and also in the Bristol Channel^ 
according to local circumstances, they rise from 
12 to 45 feet ; but it is evident that the excess 
above 12, or rather above 6, is to be attributed to 
to the resistance of the land, and the peculiar for- 
mation of the coasts, for collecting the waters of 
the ocean at that particular place* 

The waters, at a considerable distance from 
the shore, will not arrive at the shore ; they will 
only back up those that went before for some 
time, till being overpowered by the accumulated 
waters on the shore, they will return altogether 
upon the ocean by reaction, the cause which 
made them run towards the land, having now 
ceased to act. 

Suppose the sun and moon to have arrived at 
the meridian of the shore, and consequently, be- 



OF THE SEA. QJ 

ing in the line of direct gravitation of the waters 
under them, have no longer any influence upon 
those waters, as to giving motion to them, yet the 
waters will not cease running towards the shore; 
because, having been previously put in motion, 
that motion will continue, till it is somehow ov 
other overpowered. In the open ocean, the wa- 
ters appear, by the tide tables, to come to their 
greatest height about half past 2, or 3 o'clock, by 
which time then, it should seem, that the land had 
repelled the waters back towards the sea ; but if 
that should not be the case, another cau^e will 
now begin to draw them back from the land, 
.namely, the sun and moon, for by 3 o'clock, they 
will ha\e got in a position to begin to act laterally 
to draw the waters back from the shore towards 
the sea, and this action will increase more add 
luore, till the sun and moon descend below the 
horizon in the west ; their acting then ceasing, 
the waters will returnby reaction to the shore? 
and produce another tide. 

The tide which was produced by the imme- 
diate impulse of the sun and moon drawing the 
waters towards the shore, I call the direct tide? 

H 



58 THE EBBING xVND FLOWING 

or tide of impulse, and that which occurs i% 
hours after the former, I call the reactive tide, 
or tide of reaction, although, to produce this re- 
action, the luminaries sometimes concur more or 
less ; for it is the same thing whether the waters 
are drawn towards the shore, or from the shore , 
since by the laws of motion, action and reaction 
being equal with contrary directions ; it necessa- 
rily follows, that if the waters are drawn out 
from the land below their natural level, when the 
force which caused them so to ebb out, ceases 
to act, they will return towards the shore, and 
there rise above their natural level, by the resist- 
ance of the land, and so a tide must again be 
produced. 

Case S. Suppose it now to be full moon. 

In this case, though the tide of impulse of 
one luminary, does not fall in with the tide of 
impulse of the other luminary, yet it is plain that 
the tide of impulse of one, falls in with the tide 
of reaction of the other, and this reciprocally ; 
and therefore by the laws of motion, the sums or 
effects will be the same as in Case 1. 



QT THE SJSA. 59 

Case 3. Suppose the moon to be in the quad- 
ratures, or 1st or 3d quarters. 

In this case, neither the impulsive tide of one 
luminary agrees with the impulsive tide of the 
other, or with the tide of reaction of the other ; 
and therefore the tides will be much less than in 
either of the former cases. 

We must not, however, conclude, that because 
the tide in the quadratures follow the moon, that 
the sun has no band in producing them ; he has 
still by far the greatest share in producing them. 

We must always remember that the waters 
continue lateral much longer to the moon than to 
the sun, the advantage of which may be seen in 
Experiment 1 ; add to which, the moon has the 
further advantage of acting upon water already 
in motion, which it requires a less force to conti- 
nue than to originate. 

Supposing ourselves still upon a western shore, 
we must now enlarge our view of the subject* 



60 THE EBBING AND FLOWING 



PROPOSITION II. 

To shew why the tides are not so high in the 
torrid zone as they are in the temperate zone, 
the direct contrary of what has hitherto beea 
maintained. 

Hitherto we have considered the action of the 
luminaries only in the direction of east and west, 
but we will now also consider the superadded 
action in the direction of north and south, and 
indeed in the direction of every point of the com- 
pass, and rhis will at once open to us the whole 
phenomena of the tides. 

If the luminaries have more power to give mo- 
tion to the waters of the ocean, when acting in a 
line perpendicular to the line of their gravita- 
tion, than when acting in the same direction as 
the line of gravitation, we must not confine our- 
selves merely to east and west, but consider it as 
taking place equally all around at the same dis- 
tances. 



OF THE SEA. 61 

Now if we consider that the luminaries, as 
they pass over the oceans of the torrid zone, can 
ouly influence the waters immediately under 
them, or rather the waters over which they pass, 
in the direction of east and west, being unable 
to bring up in aid any waters in the direction of 
north and south, see Experiment 1, but that the 
case is quite different in the temperate zone ; for 
here not only are the waters influenced in the 
direction of east and west, but also a powerful 
aid is drawn by the same lateral action in a north 
and south direction, and this effect uniting with 
the other, the whole becomes much more consi- 
derable (see the table of ti*des.) It follows, that 
the tides must decrease from some latitude, in the 
temperate zone to the line, and this is conforma- 
able to truth. From the middle of the temperate 
zone, towards the north, the tides must fall off, 
wanting the east and west action, and depending 
only on that of north and south, and so they will 
decrease more and more, and vanish near the 
poles ; this is also conformable to the truth. 

7. We may now see that even at the quadra-* 
tures, the sun has much to do with the tides ; be- 



63 THE EBBING ANB FLOWING 

cause, the moon being either before or after him 
six hours, she may, in either case, avail herself 
(so to speak) of the waters which the sun's greater 
force is continually putting in motion ; for a body 
being jmt in motion, that motion will continue 
till stopped by some external cause, and there- 
fore the moon will find those waters still in mo- 
tion, and her effect will appear to be greater 
than what it is in reality, if left to herself; for 
this reason, as I said before, even at the quadra- 
tures, the sun has still much to do with the tides. 

It may also be observed, that as the luminaries 
pass from east to west over the torrid zone, they- 
can act only for a very short time on any given 
place within that zone, and that only in the di- 
rection of east and west, but that they can act 
very much longer on the polar and northern seas, 
even from morn to night, and therefore it is no 
wonder that the tides should be so much greater 
in the temperate than in the torrid zone. 

It is for the same reason, that the tides are 
not greatest in the torrid zone, in that particular 
latitude to which the luminaries are vertical, con- 



OF THE SEA. 63 

trary to what has been hitherto maintained. This 
fact is of itself sufficient to determine against the 
old theory, and to demonstrate this new one, 
since that old theory, built upon the falling prin- 
ciple, requires that the tides should be higher in 
that part of the torrid zone to which they are 
vertical, whereas this new theory requires just 
the contrary ; that is to say, that the tides in the 
torrid zone should be highest at one tropic, when 
the luminaries are near the other, and this is 
coniormable to the truth. 

On January 20th, 1814, there was a remarkable 
eclipse of the sun ; the luminaries were at that 
time but a few degrees from my zenith, near the 
tropic of caprieorn; the tides were very incon- 
siderable ; they increased till the full moon, July 
Sd, the same year ; the moon had nearly the same 
declination as at the time of the eclipse, but the 
sun was near the other tropic. Mow it would be 
too much to say that the moon, in this latter case, 
could do more by herself, than she could in the 
former with the assistance of the sun, according 
to the falling principle, but it would not at all 
be too much to say, that the sun could in this lat- 



64? THE EBBING AND FLOWING. 

tcr situation, give more assistance to the moony 
than he could at the time of the eclipse ; by Ex- 
periment 1, and its application, it could not be 
otherwise. And so the tide was so high as to ex- 
cite much public notice at Kio de Janeiro, and 
was by the banks thrown up for the purpose of 
repressing the tides from a salina in the neigh- 
borhood, 23 or %\ inches higher than at the 
time of the eclipse, and this difference must be 
considered as immense, where the tides at no time 
exceed five feet and a few inches. This high 
tide happened in the day, as the highest full 
moon tides always do, on this shore. Of this, 
more by and by. 

After having observed, for three years, in the 
southern part of the torrid zone, that the tides 
were not highest there when the sun and moon 
were vertical, but wiien they were at a distance 
on the other side of the zone, particularly the 
sun ; that is, the tides are highest in the winter 
months, May, June, July and August, and lowest 
in the summer months, November, December and 
January. The full moon tides, however, are the 
highest of all about July and August. After 



OF THE SEA. 



63 



having observed this, I say, for three years, I 
sought for a corresponding effect from the same 
causes, on the northern part of the torrid zone, 
and I was not long without discovering it most 
satisfactorily. At Mayo, one of the Cape de 
Verd Islands, there is a very remarkable natural 
salt work. In the winter months, when the suit 
is far away on the southern side of the torrid 
zone, the tides rise higher than usual and over- 
flow a large plain, which has no passage out again 
to the sea ; but when the sun returns to the north, 
and becomes vertical to this very place, the tides 
are not so high ; the waters of the sea do not pass 
over the natural bank into the plain, and those 
which had passed in the sun's absence, are either 
absorbed or evaporated, or more probably both, 
and leave behind a vast plain of salt ready for 
ships which choose to seek it there, and for which 
a mere trifle is paid to the Spanish governor. 
Thus we see the steady connexion between the 
cause and the effect. 

8. Having now dispatched what relates to a 

western shore, it remains to say something of an 

I 



66 THE EBBING AND FLOWING 

eastern shore, and here we shall find a difference 
most extraordinary and curious. 

PROPOSITION III. 

To shew how the tides are produced on an 
eastern shore, and why they are less on the shores 
of America, than on those of Europe and Africa. 

Case 1. Suppose it to be new moon. 

When the luminaries rise upon an eastern 
shore, they will draw the waters from the shore 
and produce an ebb, but as the luminaries acquire 
altitude, their force will decrease more and more, 
till it will vanish when they are in the meridian of 
the shore, at which time, or soon after, the waters 
will return by reaction ; and if we suppose this to 
be the first time, a small tide will be the result of 
this reaction. In the afternoon, as the luminaries 
descend towards the west, they will draw the 
waters towards the shore, and their greatest ac- 
tion being at sunset, the waters being put in mo- 
tion, mnst have time to arrive at the shore; for 
as the motion in the waters is only four or five 



OF THE SEA. 67 

miles an hour, it will take six hours for the wa- 
ters even at the small distance of 30 miles, to 
come to the shore, and so it will be midnight be- 
fore the tide of impulse on an eastern shore will 
be at the highest ; after which they will ebb out, 
and when the luminaries rise again in the morn- 
ing, their force will be to check the second re- 
action which will be taking place, and so the re- 
gular swing, oscillation or play of the waters 
will be interrupted ; and on this account they 
will not rise so high upon the land. 

On a western shore, the greatest force of the 
luminaries takes place first, i. e. when they rise 
in the horizon, but on an eastern shore, the great- 
est force takes place last, L e. when they set in, 
the horizon ; the consequence is, that there is a 
difference of nine hours on the two shores, be- 
twixt the time of the luminaries passing the me- 
ridian, and the time of high water there ; and 
therefore on an eastern shore, as that of America, 
the luminaries get round again, not to assist the 
reaction, as on the other shore, but to interrupt it 5 
and the tide of reaction being interrupted; the 



68 THE EBBING AND FLOWING 

tide of impulse will also be affected, and thus 
upon the whole, they will not rise so high. 

« 
Observe, however, that this irregularity relates 

only to the motion of the waters in an east and 
west direction, that in a north and south direction 
not being so much affected by it, hence the effect 
of this want of co-operation will be most sensible 
in the torrid zone ; and accordingly, there are 
within the torrid zone, and especially that par- 
ticular part of it where the luminaries are, but 
little tides. 

Case 2. Suppose it to be full moon. 

When the sun has descender! below the hori- 
zon in the west, and has just exerted its greatest 
force upon the waters, the moon rises to oppose 
that force with her force, and so the impulsive 
tide of the sun at mufti bg-fat will be interrupted 
and le? tied ; and when the moon has descended 
I 1 die horizon in the west, and has Just ex- 
erted her greatest force upon the waters, the sun 
will rise to oppose that force, and so the impul- 
sive tide of the moon at mid-day Will be inter- 



OF THE SEA. 69 

rupteri and lessened ; yet as the impulsive tides 
of one luminary agree and fall in with the re- 
active tides of the other, the interruption or les- 
sening upon the whole is not more than at the 
new moon, though at first sight it might seem as 
if the opposing forces would entirely extinguish 
each other. Let it be remembered also, that this 
interruption, as in Case 1, relates only to the mo- 
tion of the waters in an east and west direction, 
and therefore the effect is most sensible in the 
torrid zone, and more especially in that part of it 
where the luminaries are. 

Case 3. Suppose the moon to be in either of 
the quadratures. 

In this case, the irregularities continuing, the 
luminaries will lose that co operation which they 
had, being together, in Case 1, and that agree- 
ment of impulsive with reactive tides which took 
place in Case 2 ; and therefore the effects will be 
less than in either of those cases. Accordingly, 
by the table, the tides are less on the whole coast 
of America, and within the torrid zone, and 
more especially that part of it where the hi mi- 



70 THE EBBING AND FLOWING 

naries are, they are almost nothing. By the old 
theory, they ought to be higher here than in any 
other place ; because, beginning on the eastern 
side, and rolling on progressively to the west, 
and not being able to advance further for the 
land, they ought here to accumulate in a more 
particular manner, and their not 'doing so is ano- 
ther reason amongst so many, that that theory 
has no foundation in truth ; for in explaining 
effects from their causes, nothing must be over- 
looked ; every part must agree, and nothing dis- 
agree ; for without this, it is either not well ex- 
plained, or not well understood, or entirely with- 
out foundation. 

9. I intended to confine myself to the seeking 
only of the general principle, but I find some 
local circumstances of so much importance, that 
they cannot well be omitted. Two circumstances 
which may be called local, deserve particular 
notice. One of them goes to increase the Euro- 
pean tides, and the other to diminish the Ameri- 
can tides. It is well known to mariners, that 
there is a powerful current always setting along 
the coast of Norway, for the south, and these 



OF THE SEA. 71 

northern wafers, being thus already in motion, 
the effect of the luminaries will be much greater 
upon thein, than if there was no such motion al- 
ready begun. Now the cause of this current is 
most obvious ; all the rivers of the north of Asia 
disembogue into the northern sea; and that sea 
having no other outlet for the waters to return 
to the great oceans, this current must of neces- 
sity take place. The tides throughout all the 
British seas, are increased by this local circum- 
stance. Behold here also the polar effusions of 
St. Pierre, 

On the coast of America there is no such thing; 
nay more, there is a local circumstance which 
tends to lessen the tides there, namely, the gulf 
stream. This remarkable phenomenon, issuing 
from the gulf of Mexico, and not far from the 
American shore, widens from the land as it ad- 
vances northward, and. is yet sensible off the 
banks of Newfoundland. Now it is very evident, 
that the tides upon that shore, will be retarded 
and lessened by that powerful stream interfering 
with the action of the luminaries, and so we find 
the tides smaller than on the European side, on 



7& THE EBBIX© AND FLOWING 

this account also ; and by the table, it appears 
that the time of high water is much later, namely, 
seven o'clock, which must be understood for 
seven in the morning, for the tide of impulse at 
new moon, and seven a* night for that of full" 
moon. At Rio de Janeiro, the new and full 
moon tides take place at 2h. 30m. at the entrance 
of the harbor ; ten miles within, owing to local 
circumstances, they take place at the same time, 
and this is the place of my observations. 

Here uniformly the night tides at new mooa 
are highest, but at full moon, on the contrary, the 
day tides are highest. 

Now if this eulf stream should so interfere 
with the action of the luminaries, as to prevent 
them giving more motion to the waters of the 
ocean than 2~- miles per hour, it will take IS 
hours to bring the waters at the distance of only 
30 miles to the shore, whilst they will advance 
the same distance in six hours, at the rate of five 
miles per hour, where there is no such impe- 
diment ; and advancing slower or with less force, 
they will not only be later, but less* 



Or THE SEA. 73 

That the tides in the Pacific Ocean are less 
than in the Atlantic, is most plain, there being no 
northern seas, much less a N orway current to be 
acted upon, in aid of the merely east and west 
action. 

Finally, combine the local circumstances with 
the general principle, and you will have the sola, 
tion for any particular place. 

10. Spirit of Newton ! what sayest thou ? re- 
joice with me, for that an error is detected, and 
a new truth established in thy favorite walk. 
Tell me, great spirit, if the direct attraction was 
true, would this more powerful lateral action 
be at liberty to be overlooked and neglected ? 

The wisdom of providence, or rather of the 
Deity, is manifest in placing the luminaries at 
such exact distances, that their action, in the 
cases where they can most act on the particles 
of the others, shall only produce such moderate 
effects, as correspond with the ordinary course 
of things; thus the rivers are made to run back, 
at the same rate as they flow, and no particular 

K 



7^ THE EBBING AND FLOWING 

care is requisite to guard against the impetuosity 
of the tides ; but if the tides could be produced 
by a direct action between the luminaries and 
the waters of the ocean, then doubtless, the late- 
ral action would be so much greater, as to deluge 
the world. 

In the Newtonian theory of the tides, the moon 
is considered, from her lower position, as having 
a greater power to move the waters of the ocean 
than the sun, and yet all astronomers know that 
the earth, and every part of it, gravitate much 
more towards the sun than towards the moon. 
This contradiction arose from taking the tides, 
at the full and change, as the sum, and at the 
quadratures, as the difference of the effects of 
the sun and moon upon the waters of the sea ; 
instead of seeking the cause, from the effect truly 
observed in all latitudes, and particularly within 
the torrid zone, the cause and its manner of act- 
ing v. as assumed, and then such effects were de- 
duced from it, as would naturally follow such an 
assumption ; but when we find that these effects 
are not those of nature and truth, the assumed 



OF THE SEA. 75 

cause, or its manner of acting, necessarily falls 
to the> ground. 

The tides may be said, in a few words, to be 
the effect of the lateral gravitation of the waters 
of the ocean towards the sun, modified by the 
gravitation of the same waters towards the moon, 
according to her position with respect to any 
gi\en pUce, and are greatest at that place, at the 
full n*oon, when the sun is distant north or south 
about 45 degrees (if that can happen, because at 
this distance, the sun's action in an east and west 
direction, can unite with his action in a north 
and south direction, with the greatest effect) and 
the full moon falls between the sun and the 
place. If the sun's distance cannot be 45 de- 
grees from the place, then the greatest tides there 
will be, when the sun's distance is the greatest 
that it can be, and the full moon falls between 
the place and the sun. 

If the full moon cannot fall between the sun 
and the place, when the sun is 45 degrees from 
it, the highest tides at that place may happen 
when the sun is more distant than 45 degrees, 



76 THE EBBING AND FLOWING 

and the moon is full, as in the British seas, where 
the highest tides happen before the vernal and 
after the autumnal equinox, at full moon ; be- 
cause then the moon falls between the sun and 
the place, and is more favorably situate for act- 
ing upon the waters which have been put into 
motion by the greater force of the sun. 

It may happen that the new moon 'tides gre 
higher than the full moon tides, as is the case in 
the summer in the British seas, because the full 
moon is too far off at this season, to act upon the 
waters put into motion by the sun, especially in 
an east and west direction, which is her peculiar 
office in producing tides. She may be called the 
sun's handmaid in this business. 

With regard to the difference between day and 
night tides, I suppose it will happen everywhere 
as I found it in the torrid zone ; namely, that 
the impulsive tides will be somewhat greater 
than the reactive, the latter being a little lessened 
by friction : thus, in Europe the day tides at new 
moon, and especially in summer, will exceed the 
night tides, and the night tides at full moon, and 
especially in winter ; will exceed the day tides. 



OF THE SEA. 77 

According to the Newtonian account of the 
tides, we are told that they are highest when the 
sun and moon are in or near the equator. Where 
are they highest? at the equator ? certainly not — 
at the tropics ? no, certainly not. — where then, at 
Bristol ? yes — but how does it happen that the 
tides are not highest at Bristol, when the sun 
and moon are acting together in the northern 
tropic, &3~ degrees nearer to Bristol than they 
were at the equator? 

If the sun and moon were to decline so far as 
to become vertical at Bristol, do they not mean to 
say, that the tides would, in that case, be much 
higher there than they are now, when the sun 
and moon are in the equator ; otherwise, what 
will become of the direct influence of those bo- 
dies upon the waters of the ocean ? New as the 
tides are not so high at Bristol, when the sun 
and moon are in the northern tropic, so if they 
were to decline as far as Bristol, the tides would 
grow less and less at that place, and be no more 
(leaving out local circumstances) than they now 
are at places within the torrid zone to which the 
sun and moon are vertical, that is, about three feet, 



78 THE EBBING AND FLOWING 

which is what I found them at the southern tro- 
pic in the month of December, 

Let the philosophers consider all this, and if 
they can reconcile so many absurdities and con- 
tradictions to the old theory, let them do it; but 
if they cannot, let them give it up with a good 
grace. 

11. Drawing near to a conclusion, I shall here 
introduce another quotation from that excellent 
mathematician and philosopher. Maclaurin, who, 
in his account of Newton's discoveries, makes 
this observation upon Aristotle and his philosophy, 
namely, that he was for a long time called the 
prince of philosophers, and possessed the most 
absolute authority * in the schools. " His opi- 
nions was allowed to stand on a level with rea- 
son itself." Continues he, " it is not improper 
to have this slavish subjection of philosophers in 
remembrance; because a high esteem for great 
men, is apt to make us devoted to their opinions 
even in doubtful matters, and sometime in such 
as are foreign to philosophy." 



OF THE SEA. 79 

I will add for myself, that if a divine being 
was capable of errors in matters of science, they 
ought not to be respected, much less those of 
mortals. 

The particular observations which I may yet 
make near the southern tropic, as well as in other 
parts of the world,* will be given in a future edi- 
tion, if the publrc curiosity should call for them; 
if not, I shall rest satisfied with having given the 
general principle, and a few of the most impor- 
tant local circumstances by which the tides are 
influenced. 

* This was written in 1813. 



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